74 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



Electrodes^ 



1 



■Area A 



sensitivity, simplicity, and the absence of moving parts. Its dis- 

 advantage for a number of applications is the relatively large time 

 lag. It should be noted that the transducer sensitivity depends upon 

 the magnitude of the acceleration as well as upon its direction. If 

 one of these tubes is displaced by an angle of 10° from the vertical and 

 the output is balanced to zero, it will give a signal of 500 mV when 

 the acceleration changes by 1 g. 



For references concerning similar thermal displacement transducers (bolom- 

 eter transducers), see P. M. Pflier, "Elektrische Messung mechanischer Gros- 

 sen," 3d ed., no. 22, p. 235, Springer Verlag, Berlin, 1948. An application of 

 the thermal transducer for the measurement of sound intensity (the oscillatory 

 movement of the air cools an electrically heated wire) is described by W. S. 

 Tucker and E. T. Paris, Phil. Trans. Roy. Soc. (London), (A) 221, 389 (1920- 

 1921). 



1-25. Piezoelectric Transducers 



If a force is applied to a solid crystalline dielectric, Fig. (1-2)58, it 

 will produce stress within the crystal and a deformation of the crystal 

 lattice. In certain crystals with asymmetrical charge distributions 



(e.g., quartz), the lattice deformation 

 is, in effect, a relative displacement 

 of the positive and negative charges 

 within the lattice. The displacement 

 of the internal charges will produce 

 equal external charges of opposite 

 polarity on opposite sides of the 

 crystal (piezo-electric effect). The 

 charges can be measured by applying electrodes to the surfaces 

 and measuring the potential difference between them. 



For general literature on the piezoelectric effect, see W. P. Mason, "Piezo- 

 electric Crystals and Their Application to Ultrasonics," D. Van Nostrand Com- 

 pany, Inc., 2d ed., Princeton, N.J., 1954; W. G. Cady, "Piezoelectricity," 

 McGraw-Hill Book Company, Inc., New York, 1946; W. Voigt, "Lehrbuch 

 der Kristallphysik," Teubner Verlagsgesellschaft m.b.H., Leipzig, 1928. 



The magnitude and polarity of the induced surface charges are 

 proportional to the magnitude and direction of the applied force F. 



Q=dF (1) 



where d is a constant of the crystal (piezoelectric constant, see Table 

 5). The force F causes a thickness variation of the crystal, i.e., a 

 displacement At. The induced charge, written in terms of the dis- 

 placement A£, is n y 



Q =d _LA_t (2) 



A/ 

 Crystal - 



Fig. (1-2)58. Piezoelectric 

 schematic diagram. 



effect, 



